Research Article

Annals of Finance

, Volume 5, Issue 2, pp 189-208

First online:

On the calibration of structural credit spread models

  • Howard QiAffiliated withSchool of Business and Economics, Michigan Technological University Email author 
  • , Sheen LiuAffiliated withWashington State University-Vancouver
  • , Chunchi WuAffiliated withUniversity of Missouri-Columbia

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Empirical findings are mixed about the performance of structural models for term structure of credit spreads. It is commonly believed that all structural models have equally poor performance after calibration. However, proper calibration is not a trivial issue, especially for highly structural models. This paper proposes a more accurate procedure for calibrating two models: Leland–Toft (J Finance 51:987–1019, 1996) and Collin-Dufresne and Goldstein (J Finance 56:2177–2208, 2001). Using rating-based bond data, we find that the Leland–Toft model has significantly greater explanatory power for credit spreads across rating categories than previously reported. We provide theoretical explanations for these findings, and further extend our empirical analysis to include 286 individual senior bonds. Our findings help clarify the controversies over the performance of structural models in general and that of the Leland–Toft model in particular. In addition, we offer a rigorous procedure that can be used for calibrating other structural models more effectively.


Calibration Term structure Capital structure Default Credit spread

JEL Classification

G12 G13 G30 G32